Page 208 - Calculus Workbook For Dummies

192 Part IV: Integration and Infinite Series

You’ll get a math ticket if you put an equal sign in front of the last line because it is not equal to
the line before it. When you don’t change the limits of integration, you get this mixed-up inte-
gral with an integrand in terms of u, but with limits of integration in terms of x (s in this prob-
lem). This may be one reason why the preferred, book method includes switching the limits of
integration — it’s mathematically cleaner.

Now just antidifferentiate, switch back, and evaluate:
3 1 u 4
$
2 4
8
3 1 _ s + 5i E = 3 _ 9 - 6 i = 1974 .375
4
4
4
/ 2 3
$
2 4 8
1